I will explain how infinite sequences of flops give rise to some
interesting phenomena: first, an infinite set of smooth projective
varieties that have equivalent derived categories but are not
isomorphic; second, a pseudoeffective divisor for which...
Beauville and Voisin proved that decomposable cycles
(intersections of divisors) on a projective K3 surface span a
1-dimensional subspace of the (infinite-dimensional) group of
0-cycles modulo rational equivalence. I will address the
following...
Report on R. Virk's arXiv:1406.4855v3. This is a fun, short and
simple note with variations on the well-known theme by G. Laumon
that the Euler characteristics with and without compact supports
coincide.
I will discuss some of the topology of the fibers of proper
toric maps and a combinatorial invariant that comes out of this
picture. Joint with Luca Migliorini and Mircea Mustata.
I will outline a construction of "tropical current", a positive
closed current associated to a tropical variety. I will state basic
properties of tropical currents, and discuss how tropical currents
are related to a version of Hodge conjecture for...
The relevant preprints are: arXiv:1405.5154 "The Fano variety of
lines and rationality problem for a cubic hypersurface", Sergey
Galkin, Evgeny Shinder arXiv:1405.4902 "On two rationality
conjectures for cubic fourfolds", Nicolas Addington
Esnault asked whether a smooth complex projective variety with
infinite fundamental group has a nonzero symmetric differential,
meaning a section of some symmetric power of the cotangent bundle.
We prove a partial result in this direction, using...
In this talk I will focus on two examples of K3 categories:
bounded derived categories of (twisted) coherent sheaves and K3
categories associated with smooth cubic fourfolds. The group of
autoequivalences of the former has been intensively studied...
Cubic fourfolds behave in many ways like K3 surfaces. Certain
cubics - conjecturally, the ones that are rational - have specific
K3s associated to them geometrically. Hassett has studied cubics
with K3s associated to them at the level of Hodge...
